**Some interesting facts**

- There are 2n non-perfect square numbers between the squares of two consecutive natural numbers n and (n+1) e.g. between 2
^{2}and 3^{2}, there are

- The square number of an odd natural number n , can be expressed as the sum of two consecutive natural numbers (n
^{2}-1)/2 and (n^{2}+1)/2 e.g.

^{2}= (5

^{2}-1)/2 + (5

^{2}+1)/2.

- A triplet of three natural numbers a , b and c forms a Pythagorean Triplet , if a
^{2}+b^{2}=c^{2}e.g. (3,4,5) is a Pythagorean Triplet. For any natural number p greater than 1 , (2p , p^{2}-1 , p^{2}+1) is a Pythagorean triplet. - The squares of numbers which have all the digits as 1 , exhibit the following pattern

- Addition of two consecutive triangular numbers exhibits the following pattern :

^{2}

3 + 6 = 9 = 3

^{2}

6 + 10 = 16 = 4

^{2}

This shows that if we add two consecutive triangular numbers we get a square number.